The smallest possible area of the new rectangle is 52 square units.
In the question, we are given that a rectangle has side lengths of integral value.
We assume the lengths to be x and y units respectively, such that x and y are integers.
In the new arrangement, one pair is increased by 30%, and the other pair is decreased by 20%, such that the new sides are also integers.
We assume a 30% increase in x.
New side = x + 30% of x = x + 30/100 of x = x + 3x/10 = 13x/10.
For this to be an integer, x needs to be a multiple of 10.
Since we are considering the smallest area, we will consider the smallest multiple of 10, that is, 10 itself.
Hence, side 1 = 13 units.
We assume a 20% decrease in y.
New side = y - 20% of y = y - 20/100 of y = y - y/5 = 4x/5.
For this to be an integer, y needs to be a multiple of 5.
Since we are considering the smallest area, we will consider the smallest multiple of 5, that is, 5 itself.
Hence, side 2 = 4 units.
Now, the area of this rectangle is the product of its sides = 13*4 sq. units = 52 sq. units.
Therefore, the smallest possible area of the new rectangle is 52 square units.
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Which function represents a reflection of f(x) = 2*
Answer:
h(x)=2x-1
Step-by-step explanation:
The Given function is
f(x) =2*(0.35)* x
→y=0.7* x→Pre image
The line passes through first and third quadrant.
it is equation of straight line passing through origin and slope =0.7.
When this line is reflected over y axis , the equation of new line will be
→y= - 0.7 x⇒image
Slope of image will be = -0.7
The Image passes through Second and fourth Quadrant.
Help
NSNDNDNDN DNDNDN
Need solution ~
[tex] \sf \hookrightarrow24x =( 96 \div 2) + (55 - 50 - 4 + 5 - 6)[/tex]
[tex]24x =( 96 \div 2) + (55 - 50 - 4 + 5 - 6) \\ \\ 24 x = 48 + 0 \\ \\ 24x = 48 \\ \\ x = \frac{48}{24} \\ \\ x = 2.[/tex]
Find the value of x:
Answer:
x=20
Step-by-step explanation:
a) isolate the variable
K-8=12
10-4=6
Which expression is equivalent to[tex]18x\sqrt{14x^8}/6\sqrt{7x^4[/tex] if [tex]x\neq 0[/tex]
a. [tex]12x^4\sqrt{2}\\[/tex]
b. [tex]3x^4\sqrt{2}[/tex]
c. [tex]3x^4\sqrt{7}[/tex]
d. [tex]3x\sqrt{2}[/tex]
The equivalent expression is [tex]3x^4\sqrt{2}[/tex] . Option B
How to determine the expression
Given the expression
= [tex]\frac{18x\sqrt{14x^8} }{6\sqrt{7x^4} }[/tex]
Divide the multipliers, we have
= [tex]\frac{3x\sqrt{14x^8} }{7x^4}[/tex]
Let factorize the numerator in square root
= [tex]\frac{3x \sqrt{7x^4 * 2x^4} }{7x^4}[/tex]
Eliminate the like factor in both the numerator and denominator
= [tex]3\sqrt{2x^4}[/tex]
Let's bring forth the 'x' factor, we have
= [tex]3x^4\sqrt{2}[/tex]
Thus, the equivalent expression [tex]3x^4\sqrt{2}[/tex] . Option B
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find x
(9, x) and (3, 4); slope of -8/5
i know we have to use the formula of y2-y1/x2-x1
but it’s not working for me and i need help
Answer:
x = -5.6
Step-by-step explanation:
Using the given coordinates in the given slope formula, we have ...
(y2 -y1)/(x2 -x1) = -8/5 . . . . . using the given slope
Setup(4 -x)/(3 -9) = -8/5 . . . . substituting (9, x) for (x1, y1) and (3, 4) for (x2, y2)
SolutionMultiplying by 30, we have ...
5(x-4) = -48
5x -20 = -48 . . . . eliminate parentheses
5x = -28 . . . . . . . . add 20
x = -5.6 . . . . . . . . divide by 5
__
Additional comment
In the attachment, we have written the point-slope equation of the line, then found the point on that line that has a x-coordinate of 9. We see the y-coordinate of that point is -5.6, as computed above.
If you swap the points (x1, y1) and (x2, y2), then the slope equation ends up with fewer minus signs to handle.
(05.06 MC)
Graph the system of inequalities presented here on your own paper, then use your graph to
answer the following questions:
y > 5x + 5
y>-2x+1
Part A: Describe the graph of the system, including shading and the types of lines graphed.
Provide a description of the solution area. (6 points)
Part B: Is the point (-2, 5) included in the solution area for the system? Justify your answer
mathematically. (4 points)
(10 points)
The point (-2, 5) is not included in the solution area
The graph of the inequalitiesThe system of inequalities is given as:
y > 5x + 5
y > -2x+1
See attachment for the graph.
Since the inequalities use the greater than symbol, then the lines of the inequalities would be a dotted line and the upper part would be shaded
The solution areaThe point is given as:
(-2, 5)
The point (-2, 5) is not in the shaded area of the system of inequalities
Hence, the point is not included in the solution area
Mathematically, we have:
5 > 5 * -2 + 5 ⇒ 5 > -5 --- true
5 > -2 * -2 +1 ⇒ 5 > 5 --- false
Since both inequalities are not true, then the point is justified
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Which statement about this figure is true?
It has reflectional symmetry with one line of symmetry
It has rotational symmetry with an angle of rotation of 90%
It has no reflectional symmetry
It has no rotational symmetry
Option C. The truth statement about the figure is that it has no reflectional symmetry.
What is reflectional symmetry?
This is the term that is also used to refer to mirror symmetry. It is known to be used in respect to reflections.
The shape that we have here can be seen that it does not have this type of symmetry.
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B = 54°, c = 15, a =_?___ (Round answers to
the nearest hundredth.)
Answer:
a ≈ 8.82
Step-by-step explanation:
using the cosine ratio in the right triangle
cos54° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{a}{15}[/tex] ( multiply both sides by 15 )
15 × cos54° = a , then
a ≈8.82 ( to the nearest hundredth )
For every 3 kids movies, there will be how many horror movies?
kids movies = 24
horror= 32
Answer:
The answer will be 8
Step-by-step explanation:
SInce you notice there is movies with an 8 difference....
Answer:
4 horror movies
Step-by-step explanation:
This seems to be a problem related to ratios. We are given that, for every 24 kids' movies, there are 32 horror movies. We need to figure out how many horror movies there would be if there were just 3 kids' movies. We can set up an equation using proportions:
[tex]\frac{24}{32}=\frac{3}{x}[/tex]
We don't know how many horror movies there would be so we can let this quantity equal x. Now, we can cross multiply and solve for our unknown:
[tex]24x = 3*32\\24x = 96\\x = 4[/tex]
This means that there are 4 horror movies
In triangle ABC, < a =25
The measures of the remaining side lengths of the triangle, AC and BC is 72 units and 31 units respectively.
Angle B of the triangleB = 180 - (25 + 55)
B = 100⁰
Length of side ACsin (B)/AC = sin (C)/AB
sin (100)/AC = sin (55)/60
sin (100)/AC = 0.01365
AC = sin (100) / (0.01365)
AC = 72 units
Length side BCsin (A)/BC = sin (C)/AB
sin (25)/BC = sin (55)/60
sin (25)/BC = 0.01365
BC = sin (25) / (0.01365)
BC = 31 units
Thus, the measures of the remaining side lengths of the triangle, AC and BC is 72 units and 31 units respectively.
The complete question is below:
In triangle ABC angle A= 25, angle C= 55 and length AB = 60 . What are the approximate measures of the remaining side lengths of the triangle?
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Answer: A
Step-by-step explanation: edge2023
please help me
i dont understand this
Answer and Explanation:
Area is the measure of how large a 2-dimensional space is.
For example, a 6 × 2 grid of eggs contains 12 egg spaces.
In math, the unit for area is always a linear measurement squared (for example [tex]m^2[/tex], [tex]cm^2[/tex], and [tex]ft^2[/tex]).
Perimeter is the measurement of the border of a space.
For example, the fence around a 5 × 10 ft garden can be solved for by adding up each individual side of fencing (see the attached image).
The unit for perimeter is always a linear measurement, like m, cm, or ft.
Using this knowledge, for question a, simply multiply the side lengths to get the area. Remember to use [tex]ft^2[/tex] as the unit.
For question b, the answer is perimeter, since it is measuring the border length of the model court.
For question c, the answer is area, since it is measuring the size of the model court's wooden floor.
Use linear regression to find a
function that fits the following
points.
(0,5), (2,-13)
y = [? ]x + []
A function that fits the following points (0,5), (2,-13) is y = 9x + 5
Equation of a line
The equation of a line in slope-intercept form is expressed as;
y =mx +b
where;
m is the slope
b is the intercept
Given the following coordinates (0,5), (2,-13)
Slope = -13-5/2-0
Slope = -18/-2
Slope = 9
Since the y-intercept is b = 5, hence the equation of the line will be y = 9x + 5
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Lm=
Help me please. Thank u so much
Using circle theorem, If MN has a length of π cm, the length of LM is π√3 cm
How to find the length of LM in the circle?ΔMON = equilateral triangle.
Equilateral triangle has all its sides and angle equal to each other.
Therefore,
MN = π
Hence,
ON = MN = OM = π
ON = radius of the circle
Therefore,
LN = π+ π = 2π
Using circle theorem,
∠LMN = 90 degrees
Therefore, using Pythagoras theorem,
LM² = (2π)²- π²
LM² = 4π² - π²
LM = √3π²
LM = π√3 cm
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Complete the following constructions. leave all construction arcs on your paper.
The Dysons love to give parties. Last Friday, they gave a party and the doorbell rang 15 times. At the first ring, one guest arrived. Each time the doorbell rang after that, two more guests arrived than the time before. On Saturday they had another party. At the first ring of the doorbell a single guest arrived, at the second ring two guests appeared, at the third ring three guests and so on. If the doorbell rang 20 times Saturday night, how many guests attended? Was this party bigger than Friday's party? How do you know? 2. Draw a picture to show one way to solve this problem.
The number of guests on Saturday is 210 and it is greater than the party of Friday (15 guests)
Calculations and ParametersLast Friday had 15 guests
The sum total of guests on Saturday= 210 guests (using Arithmetic progression)
Using the arithmetic progression sum formula:
1 * 20 + (20 * 19/2) * 1= 210
Therefore, 210 > 15, so we can conclude that the Saturday night party was bigger than Friday's own.
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How do I solve y=x-2 and y=3x+5?
Answer:
x = -7/2 and y = -11/2
Step-by-step explanation:
These equations are known as slope-intercept equations.
Slope-intercept equation are a type of linear equation.
The slope-intercept format is: y = mx + b
m = the slopeb = the y-interceptBecause there are two equations, this would be a system of equations.
So, to figure this out, we need to use the substitution method.
_____________________________________________
Problem:
Solve y=x−2;y=3x+5
Solution:
Step: Solve y=x−2 for y:
Step: Substitute x-2 for y in y = 3x + 5:
y = 3x + 5
x - 2 = 3x + 5
x−2+−3x=3x+5+−3x(Add -3x to both sides)
−2x−2=5
−2x−2+2=5+2(Add 2 to both sides)
−2x=7
-2x/-2 = 7/-2 (Divide both sides by -2)
x = -7/2
Step: Substitute -7/2 for x in y = x - 2:
y = x - 2
y = -7/2 - 2
y = -11/2(Simplify both sides of the equation)
Answer:
x = -7/2 and y = -11/2
Which fraction is greater than the fraction represented by the model?
1/4
7/16
1/8
3/16
Answer:
7/16 is greater than the fraction represented by the model.
Step-by-step explanation:
The fraction represented by the model is 1/4. 7/16 is greater than 1/4 because it has a greater numerator and a smaller denominator.
Answer:
1/4 because the question is disinigrating 1/4 of my brain cells, because we can’t see the model…
Step-by-step explanation:
11. Multiple choice. Determine the volume of a cube with a side
length of 14 cm.
A. 196 cm²
12
SL
B. 196 cm³
cm
C. 14 cm²
D. 2744 cm³
3
Answer:
D
Step-by-step explanation:
the volume (V) of a cube is calculated as
V = s³ ( s is the side length ) , then
V = 14³ = 2744 cm³
Answer:
D. 2744 cm³
Step-by-step explanation:
volume can be found by multiplying length × width × height
because we know that this is a cube, all side lengths are the same (meaning length, width, and height will all be the same)
so, we know our side length is 14cm, meaning that all of our measurements {length/width/height} are 14cm
length × width × height = volume
14 × 14 × 14 = 2744
when we write volume, we write it as cubed (x³)
{similarly, when we write area, we write it as squared (x²)}
so, we would write the volume of this cube to be 2744 cm³
(option D)
hope this helps! have a lovely day :)
Select the correct answer from each drop-down menu. Graph of a four-sided polygon on a coordinate plane at A (minus 1, minus 1), B (0, 1), C (2, 2), and D (2, minus 1). In the figure, polygon ABCD is dilated by a factor of 2 to produce A′B′C′D′ with the origin as the center of dilation. Point A′ is at , and point D′ is at .
From (0, 0), the points A and D in the graph are at (-1, -1) and (2, -1) respectively.
How to depict the graph?Since the scale factor is 2, every point will be moved twice a distance in both directions. (x and y).
So, multiplying both coordinates by 2, we will get the dilated points.
Hence, A' will be at (2 × (-1), 2 × (-1)) = (-2, -2) and D' will be at (2 × 2, 2 × (-1)) = (4, -2).
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Which graph has the same end behavior as the graph of f(x)=x⁴+x³-x²-x
Using limits, a graph that goes to positive infinity when [tex]x = -\infty[/tex] and [tex]x = \infty[/tex] would have the same end behavior as the function [tex]f(x) = x^4 + x^3 - x^2 - x[/tex].
What is the end behavior of a function?It is given by it's limits as x goes to negative and positive infinity.
In this problem, the function is:
[tex]f(x) = x^4 + x^3 - x^2 - x[/tex]
The limits are:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} x^4 + x^3 - x^2 - x = \lim_{x \rightarrow -\infty} x^4 = (-\infty)^4 = \infty[/tex].[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} x^4 + x^3 - x^2 - x = \lim_{x \rightarrow \infty} x^4 = (\infty)^4 = \infty[/tex].A graph that goes to positive infinity when [tex]x = -\infty[/tex] and [tex]x = \infty[/tex] would have the same end behavior as the function [tex]f(x) = x^4 + x^3 - x^2 - x[/tex].
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what would be the right answer to 71,526 + 262
Answer:
71,788
Step-by-step explanation:
7 1 5 2 6
+ 2 6 2
____________
7 1 7 8 8
Grogg has two bags of marbles, each of which contains some red marbles and some blue marbles (and no marbles of any other color). The ratio of red marbles to blue marbles in the first bag is 3:5. The ratio of red marbles to blue marbles in the second bag is 3:2. When the two bags of marbles are mixed together, the ratio of red marbles to blue marbles is 11:9. What is the ratio of the number of marbles in the first bag to the number of marbles in the second bag?
The ratio of the number of marbles in the first bag to the number of marbles in the second bag is 2:7.
How to determine the required ratio?First of all, we would assign the variables x and y to the marbles in the first and second bag respectively. Also, let F and S represents the first and second bag respectively.
For the first bag, we have:
Ratio = 3:5 = 3x:5x = 3x + 5x = 8x
For the first bag, we have:
Ratio = 3:2 = 3y:2y = 3y + 2y = 5y
Tabulating these values, we have:
Red Blue
First bag 3x 5x
Second bag 3y 2y
The two red marbles = 3x + 3y.
The two blue marbles = 5x + 2y.
Next, we would write the ratio of the total red marbles to the total blue marbles:
Total red/Total blue = 11/9
(3x + 3y)/(5x + 2y) = 11/9
Cross-multiplying, we have:
27x + 27y = 55x + 22y
27y - 22y = 55x - 27x
5y = 28x
y = 28x/5
y = (28/5)x
y = 5.6x
Remember from the second bag, S = 5y:
S = 5(5.6x)
S = 28x.
Thus, the ratio of the number of marbles in the first bag to the number of marbles in the second bag is given by:
F/S = 8x/28x
F/S = 8/28
F/S = 2/7
F:S = 2:7.
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THE NUBER OF PEOPLE CONTACTED
Answer:
option c, x = 3
Step-by-step explanation:
Given:
f(x) = 27f(x) = [tex]3^{x}[/tex]Since both equal f(x) they must be equivalent as well,
[tex]3^{x} = 27\\[/tex]
Apply exponent rule, 3 x 3 x 3 = 27
hence x = 3
Jason has bought a new pool and has already measured some of the sides. Using the figure below and your knowledge of quadrilaterals, solve for x and y. (Round to the nearest tenth as needed.)
If Jason has bought a new pool and has already measured some of the sides. x is 16 and y is 6.
ParallelogramSolving for x using Pythagoreans theorem
5² + x² = 17²
x² = 289- 25
x = √264
x = 16
Since the shape is a parallelogram shape. Hence:
x = y
y = 16
Therefore If Jason has bought a new pool and has already measured some of the sides. x is 16 and y is 6.
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What is the correct way to represent 5600 l using scientific notation? –5.6 times. 103 l –5.6 times. 10–3 l 5.6 times. 10–3 l 5.6 times. 103 l
Answer:
5.6 x [tex]10^{3}[/tex]
Step-by-step explanation:
5600 is 5.6x10^3 in scientific notation.
5.6 x [tex]10^{3}[/tex]
Answer:
D. 5.6 × 10³ L
Edge
Which linear equation would produce a y-intercept of (0, - 7) and a slope of 5?
a.)
y = 5x - 7
b.)
y = -5x + 7
c.)
y = -7x + 5
d.)
y = 7x - 5
Answer:
a.) y = 5x - 7
Explanation:
Equation:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
insert values
[tex]\sf y - (-7) = 5(x - 0)[/tex]
simplify
[tex]\sf y + 7 = 5x[/tex]
rewrite
[tex]\sf y = 5x - 7[/tex]
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Which linear equation would produce a y-int. of (0,-7) and a slope of 5?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
Take the second co-ordinate of the point (0,-7), this is your y-intercept.
Next, just put it into y=mx+b in the place of b.
[tex]\bf{y=mx-7}[/tex] | now put in the slope, 5
[tex]\bf{y=5x-7}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=y=5x-7}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta l}}[/tex]
∞
c=pd for d pls help with steps
The given equation, when solved for d gives d = c/p
Subject of formulaeFrom the question, we are to solve for d in the given equation
The given equation is
c = pd
To solve for d, we will divide both sides by p
c/p = (pd)/p
c/p = d
∴ d = c/p
Hence, the given equation, when solved for d gives d = c/p
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The following data is organized from lowest to highest. (123, 125, 127, 141, 149, 185, 203, 215, 234, 234, 252, 279, 302, 303, 321, 327, 350, 358, 404, 425) What is the value of the median
Answer:
the median of th given data is 243
Find the missing part of the
unit rate:
21 Cards
3 Piles
=
[?] cards
Pile
Answer:
7
Step-by-step explanation:
Given,
3 Piles = 21 cards
1 Pile = (21 ÷ 3) cards
= 7 cards.
Answer:
7
Step-by-step explanation:
Because there is 7 cards in 1 pile. it follows the ratio of 7:1